Weighted material point method for managing fluid flow in pipes

Abstract

Methods and apparatus for managing fluid flow in pipes. An exemplary method includes initializing models of at least two fluid pads and one or more pipe elements, the models of the fluid pads comprising material points; for each of the material points, determining: an integration weight; and a material state; (a) for each of the fluid pads, discretizing governing fluid flow equations on a numerical grid, wherein the numerical grid is constrained within the pipe elements; (b) solving the discretized equations to generate nodal solutions; (c) constructing material point solutions from the nodal solutions; and until end criteria are met: updating the models of the fluid pads with the material point solutions; and repeating (a)-(c). An exemplary fluid flow data analysis system includes a processor and a display configured to display graphical representations of a fluid flow model, wherein the system is configured to manage fluid flow in pipes.

The invention claimed is: 
     
       1. A method for managing fluid flow in pipes, comprising:
 initializing models of at least two fluid pads and of one or more pipe elements, the models of the fluid pads comprising material points; 
 for each of the material points, determining: 
 an integration weight; and 
 a material state; 
 (a) for each of the fluid pads, discretizing governing fluid flow equations on a numerical grid, wherein the numerical grid is constrained within the pipe elements; 
 (b) solving the discretized equations to generate nodal solutions; 
 (c) constructing material point solutions from the nodal solutions; 
 updating the models of the fluid pads with the material point solutions; 
 estimating a pressure at a wellbore location represented by the models of the pipe elements based on the updated models; and 
 based on the estimated pressure, causing a pumping rate to be adjusted. 
 
     
     
       2. The method of  claim 1 , further comprising:
 measuring a pressure at a wellhead location and at a downhole location of the wellbore; and 
 calibrating at least one of the models of the fluid pads and of pipe elements with the estimated pressure and the measured pressures. 
 
     
     
       3. The method of  claim 1 , wherein the initializing the models of the fluid pads comprises at least one of:
 identification of a material type for each of the fluid pads; 
 identification of a fluid volume for each of the fluid pads; 
 identification of a density for each of the fluid pads; 
 identification of a viscosity for each of the fluid pads; 
 identification of an elasticity for each of the fluid pads; 
 identification of material properties for each of the fluid pads; 
 identification of rheological properties for each of the fluid pads; 
 identification of a solids load for each of the fluid pads; 
 identification of an order in which the fluid pads will be introduced; 
 identification of a location of introduction for each of the fluid pads; and 
 identification of a timing of introduction for each of the fluid pads. 
 
     
     
       4. The method of  claim 1 , wherein the initialization of the models of the pipe elements comprises at least one of:
 identification of a length for each of the pipe elements; 
 identification of a cross-sectional area for each of the pipe elements; 
 identification of an angle with respect to gravity for each of the pipe elements; 
 identification of a coefficient of friction of an interior surface for each of the pipe elements; and 
 identification of an order in which the pipe elements will be arranged. 
 
     
     
       5. The method of  claim 1 , wherein the constructing the material point solutions from the nodal solutions comprises interpolating the nodal solutions. 
     
     
       6. The method of  claim 1 , wherein the pipe elements represent portions of a wellbore. 
     
     
       7. A wellbore constructed by determining a bottom-hole pressure according to the method of  claim 1 , wherein the pipe elements represent portions of the wellbore, and the wellbore location is proximate a bottom of the wellbore. 
     
     
       8. A method of managing a pumping rate with the aid of a fluid flow data analysis system, the method comprising:
 obtaining data related to an initial state of a plurality of pipe elements and a plurality of fluid pads within the pipe elements; 
 generating a pumping schedule with the fluid flow data analysis system for the plurality of fluid pads through the plurality of pipe elements, the pumping schedule being adjusted based on an estimated pressure at a location in the pipe elements, the pressure being estimated by:
 initializing models of the fluid pads and of the pipe elements with the obtained data, the models of the fluid pads comprising material points; 
 for each of the material points, determining:
 an integration weight; and 
 a material state; 
 
 (a) for each of the fluid pads, discretizing governing fluid flow equations on a numerical grid, wherein the numerical grid is constrained to the pipe elements; 
 (b) solving the discretized equations to generate nodal solutions; 
 (c) constructing material point solutions from the nodal solutions;
 updating the models of the fluid pads with the material point solutions; and 
 
 adjusting the pumping rate based on the updated models. 
 
 
     
     
       9. The method of  claim 8 , wherein the pipe elements represent portions of a wellbore, the method further comprising:
 measuring a pressure at a wellhead location and at a downhole location of the wellbore; and 
 calibrating at least one of the models of the fluid pads and of pipe elements with the estimated pressure and the measured pressures. 
 
     
     
       10. The method of  claim 8 , wherein the initializing the models of the fluid pads comprises at least one of:
 identification of a material type for each of the fluid pads; 
 identification of a fluid volume for each of the fluid pads; 
 identification of a density for each of the fluid pads; 
 identification of a viscosity for each of the fluid pads; 
 identification of an elasticity for each of the fluid pads; 
 identification of material properties for each of the fluid pads; 
 identification of rheological properties for each of the fluid pads; 
 identification of a solids load for each of the fluid pads; 
 identification of an order in which the fluid pads will be introduced; 
 identification of a location of introduction for each of the fluid pads; and 
 identification of a timing of introduction for each of the fluid pads. 
 
     
     
       11. The method of  claim 8 , wherein the initialization of the models of the pipe elements comprises at least one of:
 identification of a length for each of the pipe elements; 
 identification of a cross-sectional area for each of the pipe elements; 
 identification of an angle with respect to gravity for each of the pipe elements; 
 identification of a coefficient of friction of an interior surface for each of the pipe elements; and 
 identification of an order in which the pipe elements will be arranged. 
 
     
     
       12. The method of  claim 8 , wherein the constructing the material point solutions from the nodal solutions comprises interpolating the nodal solutions. 
     
     
       13. The method of  claim 8 , wherein obtaining the data comprises measuring at least one of pressure, temperature, and flow rate at a location in the pipe elements. 
     
     
       14. A fluid flow data analysis system comprising:
 a processor; and 
 a display configured to display graphical representations of a fluid flow model, wherein the system is configured to: 
 initialize models of at least two fluid pads and of one or more pipe elements, the models of the fluid pads comprising material points; 
 for each of the material points, determine: 
 an integration weight; and 
 a material state; 
 (a) discretize governing equations on a numerical grid, wherein the numerical grid is constrained within the pipe elements; 
 (b) solve the discretized equations to generate nodal solutions; 
 (c) construct material point solutions from the nodal solutions; 
 update the models of the fluid pads with the material point solutions; 
 estimate a pressure at a wellbore location represented by the models of the pipe elements based on the updated models; and 
 cause a pumping rate to be adjusted based on the estimated pressure. 
 
     
     
       15. The system of  claim 14 , wherein the system is further configured to:
 obtain a pressure measurement at a wellhead location and at a downhole location of the wellbore; and 
 calibrate at least one of the models of the fluid pads and of pipe elements with the estimated pressure and the measured pressures. 
 
     
     
       16. The system of  claim 14 , wherein the initializing the models of the fluid pads comprises at least one of:
 identification of a material type for each of the fluid pads; 
 identification of a fluid volume for each of the fluid pads; 
 identification of a density for each of the fluid pads; 
 identification of a viscosity for each of the fluid pads; 
 identification of an elasticity for each of the fluid pads; 
 identification of material properties for each of the fluid pads; 
 identification of rheological properties for each of the fluid pads; 
 identification of a solids load for each of the fluid pads; 
 identification of an order in which the fluid pads will be introduced; 
 identification of a location of introduction for each of the fluid pads; and 
 identification of a timing of introduction for each of the fluid pads. 
 
     
     
       17. The system of  claim 14 , wherein the initialization of the models of the pipe elements comprises at least one of:
 identification of a length for each of the pipe elements; 
 identification of a cross-sectional area for each of the pipe elements; 
 identification of an angle with respect to gravity for each of the pipe elements; 
 identification of a coefficient of friction of an interior surface for each of the pipe elements; and 
 identification of an order in which the pipe elements will be arranged. 
 
     
     
       18. The system of  claim 14 , wherein the constructing the material point solutions from the nodal solutions comprises interpolating the nodal solutions. 
     
     
       19. The system of  claim 14 , wherein the pipe elements represent portions of a wellbore.